Advanced developments in the area of absorbable polymers and particularly those dealing with liquids and hydrogel-forming liquids made of copolyester and polyether-esters, respectively, were paralleled by a similarly advanced development of controlled drug delivery systems by the present inventor and coworkers for use as extrudable or injectable liquid formulations for use in parenteral and topical applications (U.S. Pat. Nos. 5,653,992; 5,714,159; 6,413,539). Pertinent to the present invention are the injectable hydrogel-forming, self-solvating, liquid, absorbable, segmented polyether-esters, which are used, in part, for the controlled release of antibacterial agents, such as doxycycline, for the treatment of periodontitis (U.S. Pat. Nos. 5,714,159; 6,413,539). The main attributes of hydrogel-forming liquid polyether-esters include their ease of application topically and as an injectable formulation without the need of using an organic solvent. However, until a recent disclosure by the present inventor (U.S. Patent Application Ser. No. 61/069,046), and in spite of the extensive development and use of segmented polyurethanes for biomedical application, the prior art was silent on the development of absorbable, segmented polyurethane compositions, which can be used independently or as part of a polymeric liquid formulation for the controlled release of a broad range of bioactive agents for use in topical, parenteral, and/or injectable applications. In effect, the only cited disclosure that is most pertinent to the instant invention is that of Shalaby et al. (U.S. Patent Application Ser. No. 61/069,046), which dealt, in part, with hydroswellable, absorbable, aliphatic segmented polyurethanes and polyurethane-ureas capable of swelling in the biological environment. Attributes associated with these polymers and the technological and clinical success of the hydrogel-forming liquid polyether-esters discussed above, provided the incentive to pursue the study associated with the present invention.